ディープラーニングに必要なデータ数の目安は？重回帰との精度を実験比較

#■■■■■■■■■■■■FIMっぽいかんじのデータを生成■■■■■■■■■■■■■■■■■
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense
from tensorflow.keras.optimizers import Adam
import matplotlib.pyplot as plt


from sklearn.preprocessing import StandardScaler

# 再現性のためのシード
np.random.seed(42)

# データ数
n = 2000

# 特徴量を人工的に作成
fim_in = np.random.randint(20, 90, n)
age = np.random.randint(40, 95, n)
mmse = np.random.randint(5, 30, n)
paralysis = np.random.randint(0, 5, n)  # 0=軽度, 1=中等度, 2=重度

# 非線形な退院時FIMの生成
# 例: sinやlogを含み、paralysisは非線形に影響
noise = np.random.normal(0, 5, n)
fim_out = (
    fim_in*2 +
    30 * np.sin(mmse/10) -
    (age - 35)**2 / 100 +
    (30 - paralysis**2)/4 +
    mmse * (6 - paralysis) + 
    noise
)

fim_out = fim_out /(fim_out.max()/126)


# データフレーム化
df = pd.DataFrame({
    'fim_in': fim_in,
    'age': age,
    'mmse': mmse,
    'paralysis': paralysis,
    'fim_out': fim_out
})

# 説明変数・目的変数に分ける
X = df[['fim_in', 'age', 'mmse', 'paralysis']]
y = df['fim_out']

# 訓練・テストに分割
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1)











# ■■■■■■サンプル数を徐々に増やしながら10回ずつ推定。平均値と標準偏差を帯状に表示。■■■■■■■■■■


sample_sizes = [50, 100,150, 200,250, 300,350, 400,450, 500,550,600,650,700,750,800]
repeat = 10

mse_lr_all = {size: [] for size in sample_sizes}
mse_dl_all = {size: [] for size in sample_sizes}

features = ['fim_in', 'age', 'mmse', 'paralysis']
target = 'fim_out'

for size in sample_sizes:
    print(size)
    for i in range(repeat):
        # サンプルサイズ分だけ取得（乱数シードを変えることで違うサンプルに）
        df_sample = df.sample(n=size, random_state=i)

        X = df_sample[features]
        y = df_sample[target]

        X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=1)

        # === 標準化 ===
        scaler = StandardScaler()
        X_train_scaled = scaler.fit_transform(X_train)
        X_test_scaled = scaler.transform(X_test)

        # 線形回帰モデル
        model_lr = LinearRegression()
        model_lr.fit(X_train_scaled, y_train)
        y_pred_lr = model_lr.predict(X_test_scaled)
        mse_lr = mean_squared_error(y_test, y_pred_lr)
        mse_lr_all[size].append(mse_lr)

        # ディープラーニングモデル
        model_dl = Sequential([
            Dense(16, activation='relu', input_shape=(X_train_scaled.shape[1],)),
            Dense(16, activation='relu'),
            Dense(1)
        ])
        model_dl.compile(optimizer=Adam(0.01), loss='mse')
        model_dl.fit(X_train_scaled, y_train, epochs=100, verbose=0, batch_size=8)

        y_pred_dl = model_dl.predict(X_test_scaled).flatten()
        mse_dl = mean_squared_error(y_test, y_pred_dl)
        mse_dl_all[size].append(mse_dl)

# 平均と標準偏差を計算
mse_lr_mean = [np.mean(mse_lr_all[size]) for size in sample_sizes]
mse_lr_std = [np.std(mse_lr_all[size]) for size in sample_sizes]
mse_dl_mean = [np.mean(mse_dl_all[size]) for size in sample_sizes]
mse_dl_std = [np.std(mse_dl_all[size]) for size in sample_sizes]

# グラフ描画
plt.figure(figsize=(12, 6))
plt.plot(sample_sizes, mse_lr_mean, label='Linear Regression MSE', color='blue')
plt.fill_between(sample_sizes, 
                 np.array(mse_lr_mean) - np.array(mse_lr_std), 
                 np.array(mse_lr_mean) + np.array(mse_lr_std), 
                 color='blue', alpha=0.2)

plt.plot(sample_sizes, mse_dl_mean, label='Deep Learning MSE', color='red')
plt.fill_between(sample_sizes, 
                 np.array(mse_dl_mean) - np.array(mse_dl_std), 
                 np.array(mse_dl_mean) + np.array(mse_dl_std), 
                 color='red', alpha=0.2)

plt.xlabel('Sample Size')
plt.ylabel('Mean Squared Error (MSE)')
plt.title('MSE vs Sample Size with Std Dev Bands (10 trials)')
plt.legend()
plt.grid(True)
plt.show()